{
  "id": "0712.2815",
  "version": "v3",
  "published": "2007-12-17T20:58:32.000Z",
  "updated": "2009-02-15T16:13:44.000Z",
  "title": "Two variants of the support problem for products of abelian varieties and tori",
  "authors": [
    "Antonella Perucca"
  ],
  "comment": "13 pages; v2 results generalized; v3 incorporated referee comments, final version to appear in Journal of Number Theory",
  "doi": "10.1016/j.jnt.2009.01.005",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-endomorphism f of G and a non-zero integer c such that f(P)=cQ. Furthermore, we are able to prove the above result with weaker assumptions: instead of comparing the order of the points we only compare the radical of the order (radical support problem) or the l-adic valuation of the order for some fixed rational prime l (l-adic support problem).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-15T16:13:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14K15",
      "14G25",
      "11R45",
      "14L10"
    ],
    "keywords": [
      "abelian variety",
      "l-adic support problem",
      "radical support problem",
      "number field",
      "non-zero integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2815P"
    }
  }
}